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Prove that the sequence {an/n} is convergent where { an} is a bounded sequence

Five hundred tickets will be sold, and these will be raffled during the town fiesta. One of these tickets will win P3,000, and the rest will win nothing. What will be the expected outcome and variance of your gain if you buy one of the tickets?

Five hundred tickets will be sold, and these will be raffled during the town fiesta. One of these tickets will win P3,000, and the rest will win nothing. What will be the expected outcome and variance of your gain if you buy one of the tickets?

A cigarette manufacturer wishes to test the claim that the variance of the nicotine content of




its cigarettes is 0.644. Nicotine content is measured in milligrams and assume that it is




normally distributed. A sample of 20 cigarettes has a standard deviation of 1.00 milligram.




At α = 0.05, is there enough evidence to reject the manufacturer’s claim?





There is a bag filled with 3 blue,2 red and 4 green marbles.A marble is taken at random from the bag,the colour is noted and then replaced.Another marble is taken at random.What is the probability of getting 2 different colours?


In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?



In a National Achievement Test, suppose three test

booklets are tested at random. Let D represent the

defective test booklet and let N represent the

non-defective test booklet. Let X be the random

variable representing the number of non-defective

test booklets



(b) Partition A = {1,2,3,4,5,6,7} rvith the minsets generated by Br = {.2,4,6} and B2 = {1,4,5} and









also find out hou' manl different subsets of A can )rou generate lrom B. and B2?

Use taylors series method to find approximate Value of y at x =0.2,given that dy/dx =2y+3ex,y(0)=0 comapre the result by solving the differential equation


Find the projection of the line segment joining the points (1, −1, 6) and (4, 3, 2) on the line (𝑥−4)/3 = −𝑦 = 𝑧/5 .


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